Nonlinear dynamics of piezoelectric nanocomposite energy harvesters under parametric resonance

This paper deals with geometrically nonlinear analysis of piezoelectric nanocomposite energy harvesters under principle parametric resonance in pre-buckling and postbuckling domains. This vibration-to-electricity conversion system consists of a bimorph piezoelectric beam under simply supported boundary conditions. The electromechanically coupled governing equations of piezoelectric composite beam are obtained based on Euler-Bernoulli beam theory and von Karman geometric nonlinearity. The material properties of nanocomposite beam are assumed to be graded in the thickness direction. The single-walled carbon nanotubes are assumed aligned, straight and a uniform layout. The Galerkin's method is employed to derive the nonlinear coupled governing equations of the problem which are then solved by using the perturbation scheme of Poincare-Lindstedt. In the numerical examples, the critical buckling load, natural frequency, postbuckling path, output voltage and the harvested power near the first principal parametric resonance under different carbon nanotube distribution pattern and volume fraction are analyzed. Numerical results showed that in the buckled configuration, the device exhibits superior power generation even within a small deviation from the critical buckling state, compared to the unbuckled state. The results also confirm that a functionally graded reinforcement has a significant influence on the bifurcation buckling, postbuckling path, natural frequencies, output voltage and harvested power of the nanocomposite beams.